Analysis of a Multilevel Dual Active Bridge (ML-DAB) DC-DC Converter Using Symmetric Modulation

Transcription

1 Electronics 215, 4, ; doi:1.339/electronics42239 Article OPEN ACCESS electronics ISSN Analysis of a Multilevel Dual Active Bridge (ML-DAB) DC-DC Converter Using Symmetric Modulation M. A. Moonem *, C. L. Pechacek, R. Hernandez and H. Krishnaswami The University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249, USA; s: cody.pechac@gmail.com (C.L.P.); rodrigo.hernandez@utsa.edu (R.H.); Hariharan.Krishnaswami@utsa.edu (H.K.) * Author to whom correspondence should be addressed; m.a.moonem@gmail.com; Tel.: ; Fax: Academic Editor: Bimal K. Bose Received: 3 January 215 / Accepted: 2 April 215 / Published: 2 April 215 Abstract: Dual active bridge (DAB) converters have been popular in high voltage, low and medium power DC-DC applications, as well as an intermediate high frequency link in solid state transformers. In this paper, a multilevel DAB (ML-DAB) has been proposed in which two active bridges produce two-level (2L)-5L, 5L-2L and 3L-5L voltage waveforms across the high frequency transformer. The proposed ML-DAB has the advantage of being used in high step-up/down converters, which deal with higher voltages, as compared to conventional two-level DABs. A three-level neutral point diode clamped (NPC) topology has been used in the high voltage bridge, which enables the semiconductor switches to be operated within a higher voltage range without the need for cascaded bridges or multiple two-level DAB converters. A symmetric modulation scheme, based on the least number of angular parameters rather than the duty-ratio, has been proposed for a different combination of bridge voltages. This ML-DAB is also suitable for maximum power point tracking (MPPT) control in photovoltaic applications. Steady-state analysis of the converter with symmetric phase-shift modulation is presented and verified using simulation and hardware experiments. Keywords: dual active bridge; DC-DC multilevel converter; neutral point clamped (NPC); symmetric modulation; soft-switching

2 Electronics 215, Introduction Because of various advantages, such as high power density, buck and boost conversion, high frequency operation, bi-directional power flow and galvanic isolation, the dual active bridge (DAB) has been widely used since the concept was first introduced in [1]. Conventionally, the DAB is a dc-dc power converter, though it has many applications in DC-AC, AC-DC [2], AC-AC [3] conversion, solid state transformers (SST) [3,4] and automotive power converters [5,6]. Most converters use the full-bridge DAB, which produces two-level (2L) square waves across the high frequency transformer. For medium and high voltage applications, DAB converters are usually cascaded [4,7] to achieve the desired high voltages due to the voltage limitation of the commercially available semiconductor switches. Experimental results, using 15-kV silicon carbide (SiC) based insulated-gate bipolar transistor (IGBT), have been reported in [8]. The multilevel DAB (ML-DAB) can overcome this voltage constraint of semiconductor switches to a great extent. The ML-DAB can be used in medium voltage (generally 2.3 kv to 6.6 kv [9]) applications without cascading or, if cascaded, can reduce the number of cascading modules in high voltage power conversion, such as high voltage direct current (HVDC) [7] applications. Power converters synthesizing more than two voltage levels, such as the neutral point clamped (NPC), cascaded H-bridge (CHB) and flying capacitor (FC), are traditionally known as multilevel converters. Usually, the multilevel topology is used in medium or high voltage inverter applications [9,1]. The CHB topology is typically used with multiple cascaded DABs to achieve higher voltages. In the CHB topology, a DAB module itself does not synthesize multilevel (e.g., 3L, 5L, 7L, and so on) voltages, like NPC or FC. Because of the simple control and modulation scheme along with the simpler circuit structure, the 3L NPC is ahead of others in various industrial applications [9]. Very few works have been published on ML-DAB. A silicon carbide junction gate field-effect transistor (SiC-JFET) based 25-kW, high switching frequency DAB has been proposed in [11], where both primary and secondary bridges produce two-level voltages, although the secondary side bridge is formed in the NPC configuration. A detailed analysis on a semi-dual active bridge (S-DAB) has been presented in [12], where the primary and secondary bridges produce 2L and 3L voltage waveforms, respectively, which are phase-shifted to control the power flow. The concept of symmetric modulation for 2L-to-5L bridge voltages with an NPC-based secondary bridge has been introduced by the authors in [13], which has the advantage of having simple mathematical representation and a minimum number of parameters to define the voltage waveforms and to control the power flow through the ML-DAB. In [14], an NPC-based multilevel DAB is reported with capacitor voltage balancing. This paper will analyze the design, modulation and power flow control of 3L NPC-based ML-DAB configurations for different cases where two active bridges produce 2L-5L, 5L-2L and 3L-5L voltage waveforms across the high frequency transformer. Section 2 discusses 3L NPC-based ML-DAB configurations with a symmetric modulation and switching scheme. Power flow equations for various ML-DAB configurations with soft-switching analysis are shown in Section 3. Section 4 discusses the applications of ML-DAB, such as maximum power point tracking (MPPT) for photovoltaic (PV) applications. Sections 5 and 6 present the simulation results and conclusions, respectively.

3 Electronics 215, ML-DAB Topologies with Symmetric Phase-Shift Modulation In this ML-DAB configuration, two bridges are assumed to have different dc voltage levels (i.e., and, where > ) where and are high and low dc bus voltages, respectively. Figures 1 and 2 show voltage step-up and step-down schematics of NPC-based 2L-5L DAB, respectively. Most DAB-based power electronic converters deal with different voltage levels at the two ends of the converter, and this ML-DAB is very suitable for such applications. If the required voltage level is much higher than the dc bus voltage, a higher voltage may be achieved by cascading multiple ML-DABs, which, in turn, facilitates conversion of large-scale (in the order of megawatts) power with a fewer number of ML-DAB modules. This methodology improves the overall efficiency and increases the power density. Phase-shift, ϕ HV dc, V P LV dc, V S S a1 S b1 S 1 S 3 S a2 S b2 V S A B i L 1 : n a L v Lk AB v o ab b High Frequency Transformer S a3 S b3 S 2 S 4 S a4 S b4 Leg-a Leg-b Figure 1. Boost configuration ( > ) of a multilevel dual active bridge (ML-DAB), where the transformer primary voltage ( ) is two-level (2L) and the secondary ( ) is of 5L. HV dc, V P Phase-shift, ϕ S a1 S b1 LV dc, V S S a2 S b2 S 1 S 3 o a S a3 b S b3 v ab i L L Lk 1 : n A High Frequency Transformer v AB S 2 B S 4 V S S a4 S b4 Leg-a Leg-b Figure 2. Buck configuration ( < ) of the ML-DAB where the transformer primary voltage ( ) is of 5L and the secondary ( ) is of 2L.

4 Electronics 215, Neutral Point Diode Clamped Configuration The neutral point diode clamp (NPC) is one of the most popular and widely-used multilevel topologies in medium and high voltage industrial applications. In this ML-DAB, three-level (3L) diode clamped legs (leg-a, b in Figures 1 and 2) are used to produce a leg-to-leg five-level (5L) voltage waveform. The low voltage bridge is switched so as to produce a two-level (2L) square waveform across the transformer. Compared to the 2L voltage source converter, the 3L-NPC configuration employs clamping diodes to connect the phase output to the neutral point o, as shown in Figures 1 and 2, which produces a 3L voltage at each NPC leg. The voltage sources (i.e.,, ) shown in Figures 1 and 2 are practically replaced by bulk capacitors, and the input and/or the output of the ML-DAB usually are followed by a source, a load or other converters in real applications. This ML-DAB can be configured for single phase or three phases with bi-directional power-flow capability by using current bi-directional switches and a suitable modulation scheme. In this paper, we are analyzing different cases of ML-DAB assuming a single-phase transformer with unidirectional power flow from the 2L bridge to the 5L bridge. The bi-directional power flow can easily be controlled with the phase-shift angle () between the active bridges. Power always flows from the voltage-leading bridge to the voltage-lagging bridge Switching States of the 3L-NPC Bridge The NPC inverter concept was first proposed in 198 [15]. Since then, researchers have contributed to several aspects of this converter, such as various modulation schemes, the number of voltage levels, capacitor voltage balancing, harmonics mitigation and active clamping instead of diodes. Switching and modulation details of a 3L-NPC as a three-phase inverter are studied in detail in [16]. In ML-DAB operation, the switching pattern of NPC is slightly different from that in conventional inverters. Unlike 3L-NPC line frequency (i.e., 5 or 6 Hz) inverters, the switching frequency is considered the fundamental frequency in an ML-DAB. Table 1 shows how a three-level voltage is synthesized in a 3L-NPC leg for both positive ( >) and negative ( <) current flow. Table 1. Switching states in a 3L-NPC leg. Status of the Switches in 3L-NPC Leg-a Switching States 3-Level LEG Voltage, ON ON OFF OFF OFF ON ON OFF OFF OFF ON ON Figure 3 shows some major switching states to form a 3L (i.e.,,, ) voltage waveform. The main advantage of the 3L-NPC is that all of the switching devices in a leg withstand only half (i.e., ) of the dc bus voltage (i.e., ) during commutation between states, which also yields lower in comparison to the two-level inverter. Switching between and states are not considered, because this scheme involves all four switches ( to ) in a leg, two being turned on and the other two being commutated off, during which dynamic voltage on each switch may not be kept the same [16]. This also causes double the switching losses. A small dead time is allowed between different states. The leg-b is

5 Electronics 215, also switched in a similar pattern to create a 3L voltage waveform. In this proposed modulation scheme, is phase-shifted from by an amount ( ) to produce a leg-to-leg 5L voltage waveform waveform across the transformer (Figure 4). Sa1 Sa2 - - Sa1 Sa2 - - Sa1 Sa2 - - Sa1 Sa2 - - o a i a o a i a o a i a o a i a Sa3 Sa4 - - Sa3 Sa4 - - Sa3 Sa4 - - Sa3 Sa4 - - v ao [] [] [] [-] - State []: S a2, S a3 ON v ao = (for i a >) v ao [] [] [] [-] - State []: S a1, S a2 ON v ao = (for i a >) v ao [] [] [] [-] - State []: S a2, S a3 ON v ao = (for i a <) v ao [] [] [] [-] - State [-]: S a3, S a4 ON v ao = - (for i a <) Figure 3. Switching states and corresponding 3L voltage ( ) synthesized from leg-a of a 3L-NPC bridge. V S π 2π v AB v ab ϕ V P -V S α β β - α -V P S a1, S a3 S a2, S a4 S b1, S b3 S b2, S b4 S 1, S 4, S 2, S 3 i L i L/n DS1, DS4, DSa3, DSa4, DSb1, DSb2 DS1, DS4, DSa3, DSa4, Sb3 S1, S4, Sa3, Sa4, Sb2 S1, S4, Sa3, Sa4, DSb3, DSb4 S1, S4, Sa3, DSb3, DSb4 S1, S4, Sa3, DSb3, DSb4 DS2, DS3, DSa1, DSa2, DSb3, DSb4 DSa1,DSa2, Sb2 Sa1,Sa2, Sb3 Sa1,Sa2, DSb1,DSb2 Sa2, DSb1,DSb2 DSa3,DSa4, DSb1,DSb2 Figure 4. Switch pulses and corresponding voltage waveforms and primary current in a 2L-5L DAB boost topology. The two-level bridge has two legs, each having two complementary switches operating with a 5% duty cycle. When, are turned on, the leg-to-leg square wave voltage =, and when, are turned on, =. Gate pulses for all twelve switches (i.e., to and to, to ) for

6 Electronics 215, both 2L and 5L bridges in a boost topology are shown in Figure 4 with the resulting voltage waveforms (, ) across the high frequency transformer and the current ( and ) through the leakage inductor Symmetric Modulation In order to synthesize the 5L voltage, the switching pulses and the resulting voltage waveform are defined with respect to angular distances (i.e.,, ) instead of the duty cycle. These angles, are measured symmetrically at zero, π and 2π within a switching period (Figure 5). The zero and are considered at the mid-point of the zero voltage level of the 5L voltage. Defining in such a symmetrical way is advantageous in terms of the minimum numbers of parameters (, ) required, which, in turn, easily describe and derive a simple mathematical expression for power flow in the ML-DAB. These parameters and shape the multilevel voltage waveform and can be utilized in the improvement of the total harmonic distortion (THD) and voltage balancing of the capacitors [14]. The phase-shift angle is independent of, and acts as the control parameter to control the power flow in the ML-DAB. v ab α β π V V P P/2 α - β -V P 2π ωt v AB V S -V S ωt <ϕ<α v AB V S α<ϕ<β -V S ωt v AB V S β<ϕ<π/2 -V S ωt Figure 5. Voltage waveforms in a 5L-2L DAB for three different cases of buck topology when is formed using =.5. In order to produce a zero-average symmetric alternating waveform, the low-voltage ( ) bridge legs should be switched complementarily at the duty cycle (D) in a range of zero to 5% ( <.5). If =.5, a 2L (, ) voltage will be formed, and if <.5, a 3L (,, ) voltage will be produced (Figure 6). This 3L voltage at the low voltage bridge is also generated symmetrically, equally spaced from zero and by an angle. This single parameter can define the 3L for the whole range of <.5. v AB γ V S π γ 2π v ab ϕ V P -V S - ωt β α α β β α -V P ωt Figure 6. Voltage waveforms in a 3L-5L DAB boost topology when is formed using <.5.

7 Electronics 215, Power Flow Equations and Soft Switching in ML-DAB In ML-DAB, power flow is controlled by the phase-shift angle () between and, like conventional DAB. The leakage inductance of the high frequency transformer acts as the main energy transfer element. This primary referred leakage inductance is assumed externally as in Figures 1 and 2. In order to analyze the power flow through each type of ML-DAB shown in Figures 4 6, we will analyze the current through the leakage inductor for each topology L-5L DAB Boost Topology The switching and modulation for a 2L-5L DAB boost topology is shown in Figure 4. The 2L is assumed to start at angle zero, and 5L is lagging by the phase-shift angle, <<. From the basic inductor voltage relation we get, =., () = 1.., () = 1.. ; where, = One switching cycle time period has been converted to 2 radians in the following equations. Now, writing this () equation for each segment of from zero to as shown in Figure 4, we get, for < < ( ): for ( ) <<( ): () =. (); ( ) =. ( ) (), (2) (1) for ( ) <<(): for () <<(): for () <<: ( ) = 2. ( ) ( ), (3) () =. ( ) ( ), (4) () = 2. ( ) (), (5) () =. ( ) 2. ( ). (2) 2 Assuming zero average current through the transformer, () = ():, 2 () =. () 2.(2 4). ( ). ( ) (), (6), () = (7) Putting this expression of (zero) in the above equations, we can get the () at different points,

8 Electronics 215, ( ) =. 2. 2, ( ) = , () = , () = The average power flow expression from the primary to secondary bridge through the leakage inductance can be written as follows: = 1 (). ()., = 2 { () ( ).( ) { ( ) ( ).( ) { ( ) ().(2) { () ().( ) { () (). ( )] After calculating the above power equation using (3), we get the simplified power equation as follows, =. 2 2 (1),.. = 2 2 ; h =, = (11) where is the average power (.. is the per unit power) measured at the output of the converter with the variables defined as, =2, where is the switching frequency, is the transformer turns ratio, is the voltage conversion ratio defined as = and is the primary referred inductance ( ) used at the high frequency link. The per unit power vs. and, while is chosen to be fixed at 1, is shown in Figure 7 for different values. Power vs. and planes with different -values for a 2L-5L DAB boost topology are shown in Figure 7. (8) (9) 2 m = 2. Output power P o, in pu m =.5 6 Phase-shift phi, in degrees Angle beta, in degrees Figure 7. ML-DAB output power.. and with = 1 for =.5, 1, 1.5 and 2.

9 Electronics 215, L-2L DAB Buck Topology The voltage waveforms for a 5L-2L DAB buck topology are shown in Figure 5. The 5L is assumed to start at angle zero, and 2L is lagging by the phase-shift angle. In this topology, based on the value of, there may be three cases, such as Case I: < <, Case II: < < and Case III: < <. Each case has been analyzed to formulate a power flow equation using the same procedure described from (1) to (11). Case I: = 1 ;< (12) Case II: = (13) Case III: = (14) Equation (14) may be considered as the generalized one and can be rewritten as follows, = ; where = (15) Equations (1) and (15) are the same, which also validates the bi-directional power-flow capability of this ML-DAB converter only based on the phase-shift between primary and secondary side bridge voltages. Figure 8 shows the power flow from the 5L to 2L bridge for the three different cases described above. Output power P o,pu Figure 8. Power flow through DAB for all three cases (12) to (14), with respect to phase-shift ; here, =1 and 2, =4 are assumed for calculation L-5L DAB Boost Topology.8.4 <φ α;α=1 o α <φ β β <φ (π/2) <φ α;α=2 o α <φ β β <φ (π/2) 45 9 Phase-shift φ in degrees The primary and secondary voltage waveforms for a 3L-5L DAB boost topology are shown in Figure 9. The 3L is assumed to start at angle after the zero, and 5L is lagging by the phase-shift angle. The pulse-width of 3L waveform is assumed symmetrically reduced by an angle of, which actually results from switch duty cycles D <.5. Using the same sector-wise inductor current analysis, as shown in (1) to (1), the power flow equation for this topology has been derived as,. = (16) If we put = in (16), it reduces to the 2L-5L power equation in (11). Similarly, if the condition is such that ==, Equations (11) and (16) reduce to the conventional two-level DAB onverter equations [1].

10 Electronics 215, V_AB Current (A) Voltage (V) Voltage (V) 2-2 2K 1K K -2K 1-1 Vab il_pri Time (s) Figure 9. Primary 3L voltage, secondary 5L voltage and current through the primary primary referred leakage inductance ; where = 29 V, =1,868 V,=1,=4, γ=2 and = Soft Switching The per unit output power vs. - characteristics is shown in Figures 1 (15), where is chosen as 15, as this value gives the minimum THD in five-level [14]. In Figure 11, the two-dimensional view of - planes ease the visualization of the boundary values of >55 and 46 for achieving soft-switching both in primary (2L) and secondary (5L) bridges, as described in the following subsections. Soft-switching boundaries in Power vs. φ - β 3D Plot 2L bridge ZVS boundary; Green plane for S1,S2,S3 & S4, 5L bridge ZVS boundaries; Blue plane for Sa1 & Sa4, Red plane for Sb1 & Sb4. m = 2 Output power P o, in pu m = Phase-shift phi, in degrees φ ~ Angle beta, in degrees Figure 1. Soft switching boundaries shown in three-dimensional power vs. - planes (where =15,< <9 and < < 9 ); the grey planes (15) show the power vs. phi-beta relations for m =.5, 1, 1.5, 2; the green plane (17) is for two-level bridge, and the zero voltage switching (ZVS) is possible while operating under this plane; the blue (18) and red (19) planes are for five-level bridge leg-a and leg-b, respectively.

11 Electronics 215, Power vs. φ-β graph (2-dimensional top view) Angle β, in degrees β ~ 46 φ ~ Phase-shift φ, in degrees 1 Figure 11. Two-dimensional view of Figure 1 showing the ZVS boundaries of and. The conventional 2L DAB topology can achieve zero voltage switching (ZVS) for all switches in the entire power range when is equal to unity. The switching pulses for the 2L-5L DAB switches are shown in Figure 4. It is possible to achieve the same in the primary bridge ( to ) with the condition of () < as shown in Figure Soft-Switching Conditions for the Two-Level ( ) Bridge From the current and voltage waveform of the switches in the primary two-level (Vs) bridge (Figure 12), we can say that the condition for soft-switching in the primary bridge should be, () <, <, < 2 2 (17) 2K 2K K -2K -3 V_AB I_Lpri 3 3 1K 2-2 1K 2-2 1K 2-2 Vab I(S 1)*1 VS 1 I(S 2)*1 VS 2 I(S 3)*1 VS 3 I(S 4)*1 VS 4 1K Time (s) Figure 12. Voltage across the transformer and, inductor current and switch currents and voltages for to.

12 Electronics 215, Soft-Switching Conditions for the Leg-a of NPC (Five-Level) Bridge Condition for Sa1 and Sa4 to be turned-on at ZVS: () >, > { 2() ( 2) (18) Boundary condition for Sb1 and Sb4 to be turned-on at ZVS: ( ) = { 2( ), = { ( ) (19) In the NPC bridge, ZVS happens in the switches,,, during turn-on at =1. The rest of the switches ( 2, 3, 2, 3 ) are also turned on at a favorable condition when the current through the switch is already zero, as shown in Figures 13 and 14. 2K K -2K 3-3 V_AB I_Lpri Vab 1K K 1K K 1K K I(Sa1)*1 I(Sa2)*1 I(Sa3)*1 VS a1 VS a2 VS a3 I(Sa4)*1 1K 1K K VS a Time (s) Figure 13. Voltage across the transformer and, inductor current and switch currents and voltages for to.

13 Electronics 215, Figure 14. Voltage across the transformer and, inductor current and switch currents and voltages for to Transformer Design V_AB 2K 2K K -2K -2K I_Lpri K 1K K 1K 1K K 1K K I(Sb1)*1 I(Sb2)*1 I(Sb3)*1 Vab VS b1 VS b2 VS b3 I(Sb4)*1 VS b4 1K 1K K Time Time (s) (s) Considering the operating frequency and loss profile, various core materials, such as silicon steel, amorphous alloy and nano-crystalline, are used as the transformer core. For frequencies less than 1 khz, the amorphous metglas material shows better performance. For this ML-DAB converter, amorphous metglas alloy 265SA1 material has been chosen in the transformer core, because of its high permeability, low core losses, high saturation flux density and narrow hysteresis curve. The design of a 3.4-kVA transformer core and winding wires has been calculated using the area-product method as shown below: The transformer core area product is defined as, = = (2) where, = 292, = 1,667, switching frequency =5, = 16.2, =2.9 (RMS values calculated from simulation results), =.5 (this factor value is chosen based on the converter topology), =.4 (this is the fill-factor having values usually within range of.3 to.6), =1 (chosen based on the maximum saturation flux density being 1.56 T), = 6 / (peak current density with the use of litz wire). From Equation (2), we get = 398,65. By using metglass 265SA1 AMCC-5 core specification, we get, = 462,, = 33, = 1,4. The conductor cross-section can be found as = =2.7, =.48. The number of turns in the transformer is calculated as,

14 Electronics 215, = = 89, and similarly = 59. AWG /36 and AWG 2 38/3 Type 2 litz wire have been chosen for transformer primary and secondary windings, respectively. 4. Applications for ML-DAB The proposed ML-DAB could find some suitable applications in a solid state transformer (SST), a front-end DC-DC converter in a photovoltaic (PV) system, a high step-up voltage DC-DC or an intermediate stage in ac-ac applications. Figure 15 shows a block diagram of the ML-DAB in a grid-connected large-scale PV system. The ML-DAB module along with inverter stage can act as a building block to be cascaded in order to achieve the 13.8-kV distribution voltage requirement. PV Solar Array Low voltage dc ML-DAB With 3-Level NPC HV bridge and High frequency transformer High voltage dc Inverter = ~ Grid Figure 15. ML-DAB module in a grid-connected photovoltaic (PV) power converter. This ML-DAB can control maximum power point tracking (MPPT) by controlling the phase-shift () between two active bridges. This topology has the advantage of being modular and replacing the bulky line frequency transformer at the grid-end with a smaller high frequency power electronic transformer. Figures 16 and 17 show the MPPT performance in an ML-DAB in PV applications. Ipv Power (W) Voltage (V) Current (A) K 2.8K 2.6K Vs Ppv (a) (b) (c) Time.12 (s).14 Time (s) Figure 16. (From top to bottom) (a) Change in PV output current Ipv due to the change in light intensity from 8 W/m 2 to 1, W/m 2 ; (b) corresponding change in voltage Vpv because of maximum power point tracking (MPPT) and (c) power Ppv.

15 Electronics 215, Power (W) Voltage (V) Current (A) K 2.8K 2.45K Ipv Figure 17. (From top to bottom) (a) Change in PV output current Ipv due to the change in light intensity from 1, W/m 2 to 8 W/m 2 ; (b) corresponding change in voltage Vpv because of MPPT and (c) power Ppv. 5. Simulation and Experimental Results Vs Ppv (a) (b) 2.1K.18.2 (c) Time.22 (s).24 Time (s) A 3.34-kW ML-DAB module with a single phase high frequency transformer has been simulated in PSIM. The design parameters of the ML-DAB are listed in Table 2. Based on the soft-switching constraints for the ML-DAB switches, as shown in (16) to (19), a good choice for modulation parameters is used for simulation, which are =1, =3 and =7. For the PV application explained in Section 4, 1,2-V or 1,7-V rated IGBTs are needed for ML-DAB. There are limitations in the switching characteristics of commercially available IGBTs when operated above 2 khz. Hence, we have chosen 5 khz for the proposed ML-DAB. The minimum input capacitor value has been theoretically calculated as 39 uf based on the ML-DAB parameters in Table 2. In the prototype, we have used a 1-uF polypropylene capacitor with a high ripple current carrying capacity. As per (1) and Table 2, the key simulation results are shown in Figures 18 and 19 for a 2L-5L DAB in the steady state. The corresponding voltage and current waveforms for the 3L-5L ML-DAB have been shown in Figure 9 for the same input, output dc voltage and power rating as shown in Table 2. The phase-shift is actually the control parameter that is controlled by a proportional-integral (PI) controller sensing the variation in input (e.g., the PV panel s output) or output (e.g., the input voltage of an inverter) dc voltages of the ML-DAB. Figures 18 and 19 show the input and output voltage, current and average power of the ML-DAB obtained from simulation.

16 Electronics 215, Table 2. Parameter values for a 3.34-kW ML-DAB based on the 2L-5L topology. Item Description Nominal Value Power rating of a ML-DAB module, 3.34 kw = () 292 V = () 1,668 V ML-DAB high frequency transformer s turns ratio, = A 2 A () 17 A Switching frequency, 5 khz Leakage Inductance for ML-DAB transformer, (value calculated as per Equation 14).5 mh 2-level PV side bridge IGBT s 6 V (49% of ) 3-level NPC bridge IGBT s 1,2 V (7% of Soft-switching results for semiconductor switches in the converter are shown in Figures showing zero voltage switching (ZVS) and zero current switching (ZCS) performance. Infineon 1,2-V IGBT modules FF1R12YT3 are modeled in the simulation to estimate the losses and efficiency. In the simulation, the conduction losses have been modelled based on the IGBT datasheet parameters and assuming linear switching characteristics. The efficiency is 96.42%, as seen in the simulation. V_AB Current (A) Voltage (V) Voltage (V) 2-2 2K 1K K -2K 2-2 Vab I_Lpri (a) (b) Time.298 (s) Time (s) Figure 18. (From top to bottom) (a) Primary 2L voltage ; (b) secondary 5L voltage ; and (c) current through the primary referred leakage inductor. (c)

17 Electronics 215, Power (W) Current (A) Current (A) , 3 3, 2 2, 1 1, Iin AVG(Iin) Io AVG(Io) AVG(Iin*Vs) (a) (b) AVG(Io*Vp) (c) Time.298 (s) Time (s) Figure 19. (From top to bottom) (a) ML-DAB input current and its average; (b) output current and its average; and (c) average input and output power =( ) and =( ). Simulation and experimental results also verify the functionality of the proposed ML-DAB and the symmetric modulation technique. A hardware prototype (Figure 2) has been built and tested with a scaled-down input voltage ( = 12 V, =5 khz) to verify the power flow and open-loop control. The gate signal for all the twelve IGBTs used in the ML-DAB is shown in Figure 21.The experimental voltage and current waveforms shown in Figures 22 and 23 have a close match with the simulation results shown in Figures 18 and 19. Figure 24 shows the output voltage and current waveforms when the ML-DAB is connected to a full-bridge inverter and a resistive-inductive (R-L) load. In the hardware prototype, an overall efficiency of 88% (Figure 25) has been observed for a 12-V input voltage and 638 W (which is 2% of the rated power of the converter) of input power (Table 3). At full rated power, it is expected that the observed efficiency will closely match with the theoretical and simulated efficiency figures. 2 level Bridge HF Transformer 5 level NPC Bridges Figure 2. ML-DAB prototype hardware setup for laboratory testing.

18 Electronics 215, Figure 21. Gate pulses for the ML-DAB IGBTs (from top to bottom:,,, and,,, and,,, ). Table 3. Experimental efficiency and losses for the prototype ML-DAB. (V) (V) (w) (w) (w) (w) (%) (%) Figure 22. ML-DAB 2L voltage, 5L voltage and current through the 2L and 5L side of the transformers and ; where = 125 V, = 65 V, = 5.71, = 1, =3 and = 7.

19 Electronics 215, ML-DAB 2-Level bridge dc current ML-DAB NPC 5L bridge dc current Figure 23. ML-DAB input (2L bridge) and output (5L bridge) dc current waveforms and. Inverter output voltage Inverter output current Figure 24. Output voltage and current waveforms when the ML-DAB is connected to a full-bridge inverter and a resistive-inductive (R-L) load.

20 Electronics 215, Efficiency curve of ML-DAB and transformer Output Power (W) Eff.trans (%) Eff.total (%) Figure 25. Efficiency curve of the transformer and ML-DAB with output power variation. 6. Conclusions In this paper, a multilevel DAB (ML-DAB) dc-dc converter has been proposed for its use in high step-up/down, high-voltage applications. The boost and buck configurations of the ML-DAB have been explained in detail. A symmetric modulation technique has been proposed, which allows for independent control of the phase-shift from the control parameters that shape the multilevel voltage waveforms. The paper analyzes in detail the 2L-5L, 5L-2L and 3L-5L voltage waveforms across the high frequency transformer and derives expressions for the power flow. A soft-switching analysis along with boundary conditions is presented. The converter is designed and simulated in PSIM. A hardware prototype is built and tested to verify the proposed ML-DAB performance with the symmetric modulation scheme. Experimental results have been presented to validate the proposed modulation and power flow in the ML-DAB. Acknowledgments This work is supported by the United States Department of Energy under Award No. DE-EE6323. Author Contributions M.A. Moonem and H. Krishnaswami conceived the concept, performed the analysis and designed the experiments. R. Hernandez and C. Pechacek designed the prototype and performed the experiments; R. Hernandez and H. Krishnaswami analyzed the data; M.A. Moonem wrote the paper; All authors approved the final manuscript. Conflicts of Interest The authors declare no conflict of interest.

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